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  1. added 2020-05-27
    The Definition of Number.Hartley Burr Alexander - 1915 - The Monist 25 (3):365-398.
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  2. added 2020-05-19
    Entscheidbarkeit der Arithmetik MIT Addition Und Ordnung in Logiken MIT Verallgemeinerten Quantoren.Helmut Wolter - 1975 - Mathematical Logic Quarterly 21 (1):321-330.
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  3. added 2020-05-19
    Zur Benutzung der Verkettung Als Basis Für Die Arithmetik.Michael Deutsch - 1975 - Mathematical Logic Quarterly 21 (1):145-158.
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  4. added 2020-05-19
    Ist Die Arithmetik Ein Logisch Korrektes Lehrgebäude?Wilhelm Koppelmann - 1929 - Annalen der Philosophie Und Philosophischen Kritik 6 (1):41-53.
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  5. added 2020-05-14
    On Different Ways of Being Equal.Bruno Bentzen - forthcoming - Erkenntnis.
    The aim of this paper is to present a constructive solution to Frege's puzzle (largely limited to the mathematical context) based on type theory. Two ways in which an equality statement may be said to have cognitive significance are distinguished. One concerns the mode of presentation of the equality, the other its mode of proof. Frege's distinction between sense and reference, which emphasizes the former aspect, cannot adequately explain the cognitive significance of equality statements unless a clear identity criterion for (...)
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  6. added 2020-03-13
    Revisão de ‘Eu sou um Loop Estranho’ (I am a Strange Loop) por Douglas Hofstadter (2007) (revisão revisada 2019).Michael Richard Starks - 2020 - In Entendendo as Conexões entre Ciência, Filosofia, Psicologia, Religião, Política, Economia, História e Literatura - Artigos e Avaliações 2006-2019. Las Vegas, NV USA: Reality Press. pp. 251-268.
    Último sermão da Igreja do naturalismo fundamentalista pelo pastor Hofstadter. Como o seu muito mais famoso (ou infame por seus erros filosóficos implacáveis) Godel, Escher, Bach, ele tem uma plausibilidade superficial, mas se se compreende que este é um cientificismo desenfreado que mistura questões científicas reais com os filosóficos (ou seja, o somente as edições reais são que jogos da língua nós devemos jogar) então quase todo seu interesse desaparece. Eu forneci um quadro para análise baseada na psicologia evolutiva e (...)
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  7. added 2020-02-11
    The Philosophy of Mathematics Today.Fraser MacBride - 2003 - Mind 112 (448):792-799.
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  8. added 2020-02-11
    Physics and Metaphysics of Music, and Essays on the Philosophy of Mathematics. Lazare Saminsky.E. F. Kaelin - 1958 - Philosophy of Science 25 (4):309-309.
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  9. added 2020-02-01
    Papineau's Philosophical Devices [Review]. [REVIEW]Matheus Silva - 2012 - Fundamento 5:147-150.
  10. added 2020-01-04
    Deleuze on Leibniz : Difference, Continuity, and the Calculus.Daniel W. Smith - 2005 - In Current Continental Theory and Modern Philosophy. Northwestern University Press.
  11. added 2019-12-22
    Revisão de ' Os Limites Exteriores da Razão ' (The Outer Limits of Reason)Por Noson Yanofsky 403p (2013) (Revisão Revisada 2019).Michael Richard Starks - 2019 - In Delírios Utópicos Suicidas no Século XXI Filosofia, Natureza Humana e o Colapso da Civilization- Artigos e Comentários 2006-2019 5ª edição. Las Vegas, NV USA: Reality Press. pp. 188-202.
    Eu dou uma revisão detalhada de "os limites exteriores da razão" por Noson Yanofsky de uma perspectiva unificada de Wittgenstein e psicologia evolutiva. Eu indico que a dificuldade com tais questões como paradoxo na linguagem e matemática, incompletude, undecidabilidade, computabilidade, o cérebro eo universo como computadores, etc., todos surgem a partir da falta de olhar atentamente para o nosso uso da linguagem no apropriado contexto e, consequentemente, a falta de separar questões de fato científico a partir de questões de como (...)
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  12. added 2019-12-21
    O que significa paraconsistente, indecível, aleatório, computável e incompleto?- Uma revisão da ‘Godel’s Way: exploits into an undecidable world’ (Maneira de Godel: façanhas em um mundo indecidível) por Gregory Chaitin, Francisco A Doria, Newton C.A. da costa 160P (2012) (revisão revisada 2019).Michael Richard Starks - 2019 - In Delírios Utópicos Suicidas no Século XXI Filosofia, Natureza Humana e o Colapso da Civilization- Artigos e Comentários 2006-2019 5ª edição. Las Vegas, NV USA: Reality Press. pp. 168-182.
    Em "Godel's Way", três cientistas eminentes discutem questões como a undecidability, incompletude, aleatoriedade, computabilidade e paraconsistência. Eu abordar estas questões do ponto de vista Wittgensteinian que existem duas questões básicas que têm soluções completamente diferentes. Há as questões científicas ou empíricas, que são fatos sobre o mundo que precisam ser investigados observacionalmente e questões filosóficas sobre como a linguagem pode ser usada inteligìvelmente (que incluem certas questões em matemática e lógica), que precisam ser decidido por olhar uma como nós realmente (...)
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  13. added 2019-12-19
    Aplicabilitatea matematicii ca problema filosofica.Gabriel Târziu - 2013 - Iași, Romania: Institutul European Publishing House.
    In aceasta lucrare, autorul si-a propus sa readuca in discutie problema aplicabilitatii matematicii - atat de importanta pentru Kant, dar care a ajuns sa fie in mare parte neglijata in filosofia contemporana a matematicii - incercand sa argumenteze, plecand de la ea, pentru o viziune empirista in filosofia matematicii. Strategia pe care autorul isi propune sa o urmeze, in linii mari, consta intr-o incercare de a atrage atentia asupra unei probleme care apare atunci cand avem in vedere utilitatea matematicii in (...)
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  14. added 2019-11-29
    Reseña de 'The Outer Limits of Reason' por Noson Yanofsky 403p (2013).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 71-90.
    Doy una revisión detallada de ' los límites externos de la razón ' por Noson Yanofsky desde una perspectiva unificada de Wittgenstein y la psicología evolutiva. Yo indiqué que la dificultad con cuestiones como la paradoja en el lenguaje y las matemáticas, la incompletitud, la indeterminación, la computabilidad, el cerebro y el universo como ordenadores, etc., surgen de la falta de mirada cuidadosa a nuestro uso del lenguaje en el adecuado contexto y, por tanto, el Error al separar los problemas (...)
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  15. added 2019-11-29
    ¿Qué significa paraconsistente, indescifrable, aleatorio, computable e incompleto? Una revisión de la Manera de Godel: explota en un mundo indecible (Godel’s Way: exploits into an undecidable world) por Gregory Chaitin, Francisco A Doria, Newton C.A. da Costa 160P (2012) (revisión revisada 2019).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 44-63.
    En ' Godel’s Way ', tres eminentes científicos discuten temas como la indecisión, la incompleta, la aleatoriedad, la computabilidad y la paraconsistencia. Me acerco a estas cuestiones desde el punto de vista de Wittgensteinian de que hay dos cuestiones básicas que tienen soluciones completamente diferentes. Existen las cuestiones científicas o empíricas, que son hechos sobre el mundo que necesitan ser investigados observacionalmente y cuestiones filosóficas en cuanto a cómo el lenguaje se puede utilizar inteligiblemente (que incluyen ciertas preguntas en matemáticas (...)
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  16. added 2019-11-29
    Wolpert, Chaitin y Wittgenstein sobre la imposibilidad, la incompletitud, la paradoja mentirosa, el teísmo, los límites de la computación, un principio de incertidumbre mecánica no cuántica y el universo como computadora, el teorema definitivo en la teoría de la máquina de Turing (revisado en 2019).Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 64-70.
    It is commonly thought that Impossibility, Incompleteness, Paraconsistency, Undecidability, Randomness, Computability, Paradox, Uncertainty and the Limits of Reason are disparate scientific physical or mathematical issues having little or nothing in common. I suggest that they are largely standard philosophical problems (i.e., language games) which were mostly resolved by Wittgenstein over 80years ago. -/- “What we are ‘tempted to say’ in such a case is, of course, not philosophy, but it is its raw material. Thus, for example, what a mathematician is (...)
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  17. added 2019-11-29
    Reseña de ‘Soy un Bucle Extraño’ ( I am a Strange Loop) de Douglas Hofstadter.Michael Richard Starks - 2019 - In Observaciones Sobre Imposibilidad, Incompleta, Paracoherencia,Indecisión,Aleatoriedad, Computabilidad, Paradoja E Incertidumbre En Chaitin, Wittgenstein, Hofstadter, Wolpert, Doria, Dacosta, Godel, Searle, Rodych, Berto,Floyd, Moyal-Sharrock Y Yanofsky. Las Vegas, NV USA: Reality Press. pp. 21-43.
    Último sermón de la iglesia del naturalismo fundamentalista por el pastor Hofstadter. Al igual que su mucho más famoso (o infame por sus incesantemente errores filosóficos) trabajo Godel, Escher, Bach, tiene una plausibilidad superficial, pero si se entiende que se trata de un científico rampante que mezcla problemas científicos reales con los filosóficos (es decir, el sólo los problemas reales son los juegos de idiomas que debemos jugar) entonces casi todo su interés desaparece. Proporciono un marco para el análisis basado (...)
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  18. added 2019-10-14
    Immobility Theory.Ninh Khac Son - manuscript
    The content of the manuscript represents a bold idea system, it is beyond the boundaries of all existing knowledge but the method of reasoning and logic is also very strict and scientific. The purpose of the manuscript is to unify the natural categories (natural philosophy, natural geometry, quantum mechanics, astronomy,…), and to open a new direction for most other sciences. Abstract of the manuscript: About Philosophy: • Proved the existence of time and non-dilation. • Proved that matter is always motionless (...)
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  19. added 2019-09-26
    Science and Hypothesis: The Complete Text by Henri Poincaré (New Translation).Mélanie Frappier, Andrea Smith & David J. Stump (eds.) - 2017 - London: Bloomsbury.
    New Translation of Henri Poincaré's Science and Hypothesis, including new material and editorial commentary. New Introduction by David J. Stump.
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  20. added 2019-09-15
    Research in History and Philosophy of Mathematics The CSHPM 2017 Annual Meeting in Toronto, Ontario.Maria Zack & Dirk Schlimm (eds.) - 2018 - New York: Birkhäuser.
    This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. -/- A series of chapters all set in the eighteenth century consider topics such as John Marsh’s (...)
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  21. added 2019-08-25
    A Structuralist Proposal for the Foundations of the Natural Numbers.Desmond A. Ford - manuscript
    This paper introduces a novel object that has less structure than, and is ontologically prior to the natural numbers. As such it is a candidate model of the foundation that lies beneath the natural numbers. The implications for the construction of mathematical objects built upon that foundation are discussed.
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  22. added 2019-07-30
    What Types Should Not Be.Bruno Bentzen - 2020 - Philosophia Mathematica 28 (1):60-76.
    In a series of papers Ladyman and Presnell raise an interesting challenge of providing a pre-mathematical justification for homotopy type theory. In response, they propose what they claim to be an informal semantics for homotopy type theory where types and terms are regarded as mathematical concepts. The aim of this paper is to raise some issues which need to be resolved for the successful development of their types-as-concepts interpretation.
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  23. added 2019-07-02
    Sofia A. Yanovskaya: The Marxist Pioneer of Mathematical Logic in the Soviet Union.Dimitris Kilakos - 2019 - Transversal: International Journal for the Historiography of Science 6:49-64.
    K. Marx’s 200th jubilee coincides with the celebration of the 85 years from the first publication of his “Mathematical Manuscripts” in 1933. Its editor, Sofia Alexandrovna Yanovskaya (1896–1966), was a renowned Soviet mathematician, whose significant studies on the foundations of mathematics and mathematical logic, as well as on the history and philosophy of mathematics are unduly neglected nowadays. Yanovskaya, as a militant Marxist, was actively engaged in the ideological confrontation with idealism and its influence on modern mathematics and their interpretation. (...)
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  24. added 2019-06-06
    A Ludic Book on Ludic Proof * Reviel Netz. Ludic Proof, Greek Mathematics and Alexandrian Aesthetic. Cambridge: Cambridge University Press, 2009. ISBN 978-0-521-89894-2. Pp. Xvi + 255. [REVIEW]Ladislav Kvasz - 2011 - Philosophia Mathematica 19 (1):91-95.
    The latest book of Reviel Netz presents a highly erudite analysis of the style of Hellenistic mathematics. Besides the Introduction and Conclusion the book is composed of four chapters. Before turning to more general remarks I would like first to outline the contents of the book.The Introduction starts with the presentation of Archimedes’ Spiral lines. In a condensed form, the author outlines his approach and calls attention to the stylistic peculiarities of that work. Most of the themes discussed in more (...)
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  25. added 2019-06-06
    Jody Azzouni. Talking About Nothing. New York: Oxford University Press, 2010. ISBN 978-0-19-973894-64. Pp. Iv + 273†. [REVIEW]Graham Priest - 2011 - Philosophia Mathematica 19 (3):359-363.
    Our normal discourse is replete with discussion of things which do not exist — the objects of fiction, of illusion and hallucination, of religious worship, of misguided fears and other intentional states. Let us call such discourse empty. How to account for the meaning of empty discourse, and such truth values as its statements have, are perennial and thorny philosophical topics. Many positions are well known; in this book of five chapters Azzouni advocates another. Empty discourse is literally about nothing; (...)
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  26. added 2019-06-06
    Discovery, Invention and Realism: Gödel and Others on the Reality of Concepts.Michael Detlefsen - 2011 - In John Polkinghorne (ed.), Mathematics and its Significance. Oxford: Oxford University Press. pp. 73-96.
    The general question considered is whether and to what extent there are features of our mathematical knowledge that support a realist attitude towards mathematics. I consider, in particular, reasoning from claims such as that mathematicians believe their reasoning to be part of a process of discovery (and not of mere invention), to the view that mathematical entities exist in some mind-independent way although our minds have epistemic access to them.
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  27. added 2019-06-06
    Stephen Pollard Ed. Essays on the Foundations of Mathematics by Moritz Pasch. The Western Ontario Series in Philosophy of Science; 83. Dordrecht: Springer, 2010. ISBN 978-90-481-9415-5 . Pp. Xi &Plus; 245: Critical Studies/Book Reviews. [REVIEW]S. Gandon - 2011 - Philosophia Mathematica 19 (3):354-359.
    Moritz Pasch is usually seen today as a precursor of Hilbert. The Vorlesungen über neuere Geometrie is indeed one of the few works Hilbert referred to in the Grundlagen. Unfortunately, Hilbert's epoch-making book has eclipsed Pasch's achievement; so much so that Pasch's Vorlesungen has not been yet translated into English. But as Pollard emphasizes, it would be a mistake to reduce Pasch's research to his work on the foundations of geometry. Pasch published another book on the foundations of real analysis (...)
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  28. added 2019-06-06
    Forms of Mathematization.Sophie Roux - 2010 - Early Science and Medicine 15 (4-5):319-337.
    According to a grand narrative that long ago ceased to be told, there was a seventeenth century Scientific Revolution, during which a few heroes conquered nature thanks to mathematics. When this grand narrative was brought into question, our perspectives on the question of mathematization should have changed. It seems, however, that they were instead set aside, both because of a general distrust towards sweeping narratives that are always subject to the suspicion that they overlook the unyielding complexity of real history, (...)
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  29. added 2019-06-06
    Paolo Mancosu, Ed. The Philosophy of Mathematical Practice. Oxford: Oxford University Press, 2008. ISBN 978-0-19-929645-3. Pp. Xi &Plus; 447: Critical Studies/Book Reviews. [REVIEW]Brendan Larvor - 2010 - Philosophia Mathematica 18 (3):350-360.
    (No abstract is available for this citation).
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  30. added 2019-06-06
    Tomasz Placek. Mathematical Intuitionism and Intersubjectivity. A Critical Exposition of Arguments for Intuitionism. Dordrecht: Kluwer Academic Publishers, 1999. Pp. Xii + 218. ISBN 0-7923-5630-6. [REVIEW]Menno Lievers - 2004 - Philosophia Mathematica 12 (2):176-186.
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  31. added 2019-06-06
    Review of Kurt Gödel Collected Works IV–V: Correspondence.Jan von Plato - 2004 - Bulletin of Symbolic Logic 10 (4):558-563.
  32. added 2019-06-06
    Introduction.Juliette Kennedy & Gabriel Sandu - 2003 - Synthese 137 (1):1-1.
  33. added 2019-06-06
    Philosophies of Mathematics.Alexander George & Daniel J. Velleman - 2002 - Blackwell.
    This book provides an accessible, critical introduction to these three projects as it describes and investigates both their philosophical and their mathematical ...
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  34. added 2019-06-06
    Alternative Mathematics: The Vague Way.Jean Paul Van Bendegem - 2000 - Synthese 125 (1):19-31.
    Is alternative mathematics possible? More specifically, is it possible to imagine that mathematics could have developed in any other than the actual direction? The answer defended in this paper is yes, and the proof consists of a direct demonstration. An alternative mathematics that uses vague concepts and predicatesis outlined, leading up to theorems such as "Small numbers have few prime factors''.
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  35. added 2019-06-06
    Review of What Is Mathematics, Really? By Reuben Hersh. [REVIEW]Michael Liston - 1999 - Philosophy of Science 66 (3):501-502.
  36. added 2019-06-06
    Critical Notice. Godel's Philosophical Remarks on Logic and Mathematics.R. Tieszen - 1998 - Mind 107 (425):219-232.
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  37. added 2019-06-06
    Review of Notes on Philosophy, Probability and Mathematics by Frank Plumpton Ramsey; Maria Carla Galavotti. [REVIEW]Maria Concetta Di Maio - 1994 - Philosophy of Science 61 (3):487-489.
  38. added 2019-06-06
    On the Failure of Mathematics' Philosophy: Review of P. Maddy, Realism in Mathematics; and C. Chihara, Constructibility and Mathematical Existence.David Charles McCarty - 1993 - Synthese 96 (2):255-291.
  39. added 2019-06-06
    Meaning and Existence in Mathematics. [REVIEW]F. K. C. - 1974 - Review of Metaphysics 27 (4):790-791.
    This ninth volume in the Library of Exact Philosophy series is a development of the author’s 1971 McGill University dissertation written under the guidance of Mario Bunge. The thesis of the book is that the objectivity of mathematics does not require that there be any mathematical objects. The objectivity of mathematics is the widespread agreement among working mathematicians on what is provable, i.e., on what entailments hold between mathematical constructs. Castonguay gives precise definitions of several terms; but, unfortunately, "construct" is (...)
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  40. added 2019-06-06
    The Instrumentalist and Formalist Elements of Berkeley's Philosophy of Mathematics.Robert J. Baum - 1972 - Studies in History and Philosophy of Science Part A 3 (2):119.
    The main thesis of this paper is that, Contrary to general belief, George berkeley did in fact express a coherent philosophy of mathematics in his major published works. He treated arithmetic and geometry separately and differently, And this paper focuses on his philosophy of arithmetic, Which is shown to be strikingly similar to the 19th and 20th century philosophies of mathematics known as 'formalism' and 'instrumentalism'. A major portion of the paper is devoted to showing how this philosophy of mathematics (...)
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  41. added 2019-06-06
    Aristotle’s Notion of Quantity and Modern Mathematics.Seamus Hegarty - 1969 - Philosophical Studies (Dublin) 18:25-35.
    THE notion of quantity is basic and it is no surprise that Aristotle refers to it in many places. There are two main discussions, that in the Categories—a part of the Organon which is of great interest to modern logicians and that spread over the physical treatises. Naturally the two treatments overlap, but modern logic is at a far remove from classical cosmology and it is fairly easy to separate them at their sources. This I have attempted to do by (...)
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  42. added 2019-06-06
    On the New Foundational Crisis of Mathematics.Herman Weyl - 1921 - In P. Mancosu (ed.), ¸ Itemancosu1998. Oxford University Press. pp. 86--118.
  43. added 2019-06-06
    Oughtred’s Ideas and Influence on the Teaching of Mathematics.Florian Cajori - 1915 - The Monist 25 (4):495-530.
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  44. added 2019-06-05
    A Not So Fine Modal Version of Generality Relativism.Gonçalo Santos - 2010 - Theoria : An International Journal for Theory, History and Fundations of Science 25 (2):149-161.
    The generality relativist has been accused of holding a self-defeating thesis. Kit Fine proposed a modal version of generality relativism that tries to resist this claim. We discuss his proposal and argue that one of its formulations is self-defeating.
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  45. added 2019-06-05
    Mathematical Concepts and Proofs From Nicole Oresme.Jeff Babb - 2005 - Science & Education 14 (3-5):443-456.
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  46. added 2019-06-05
    Review Essay: Reflections on Kurt GodelReflections on Kurt Godel.Palle Yourgrau & Hao Wang - 1989 - Philosophy and Phenomenological Research 50 (2):391.
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  47. added 2019-06-05
    The Philosophy of Mathematics. Edward A. Maziarz.Erwin Biser - 1957 - Philosophy of Science 24 (4):357-357.
  48. added 2019-06-05
    The Basic Concepts of Mathematics. Karl Menger.J. Richard Buchi - 1957 - Philosophy of Science 24 (4):366-366.
  49. added 2019-05-31
    Hilary Putnam. Mathematics Without Foundations. The Journal of Philosophy, Vol. 64 , Pp. 5–22.Georg Kreisel - 1972 - Journal of Symbolic Logic 37 (2):402-404.
  50. added 2019-05-07
    La scoperta scientifica: la ricerca di un metodo e il suo smarrimento.Emiliano Ippoliti - 2019 - In Stefano Velotti & Luigi Conti (eds.), Strumenti del Pensiero. Vol. 2. Rome: Laterza. pp. 935-964.
    (ENG) The paper examines the first attempts put forward in ancient Greek to build a method for scientific discovery and how they have been progressively neglected. -/- (ITA) L'articolo esamina i primi tentativi effettuati nell'antica grecia di costruire un metodo della scoperta scientifica, e analizza le ragioni che hanno portato al suo progessivo abbandono.
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